family {stats}  R Documentation 
Family objects provide a convenient way to specify the details of the
models used by functions such as glm
. See the
documentation for glm
for the details on how such model
fitting takes place.
family(object, ...) binomial(link = "logit") gaussian(link = "identity") Gamma(link = "inverse") inverse.gaussian(link = "1/mu^2") poisson(link = "log") quasi(link = "identity", variance = "constant") quasibinomial(link = "logit") quasipoisson(link = "log")
link 
a specification for the model link function.
The gaussian family accepts the links "identity" ,
"log" and "inverse" ;
the binomial family the links "logit" ,
"probit" , "cauchit" , (corresponding to logistic,
normal and Cauchy CDFs respectively) "log" and
"cloglog" (complementary loglog);
the Gamma family the links "inverse" , "identity"
and "log" ;
the poisson family the links "log" , "identity" ,
and "sqrt" and the inverse.gaussian family the links
"1/mu^2" , "inverse" , "identity" and "log" .
The quasi family allows the links "logit" , "probit" ,
"cloglog" , "identity" , "inverse" ,
"log" , "1/mu^2" and "sqrt" .
The function power can also be used to create a
power link function for the quasi family.

variance 
for all families, other than quasi , the
variance function is determined by the family. The quasi
family will accept the specifications "constant" ,
"mu(1mu)" , "mu" , "mu^2" and "mu^3" for
the variance function. 
object 
the function family accesses the family
objects which are stored within objects created by modelling
functions (e.g., glm ). 
... 
further arguments passed to methods. 
The quasibinomial
and quasipoisson
families differ from
the binomial
and poisson
families only in that the
dispersion parameter is not fixed at one, so they can “model”
overdispersion. For the binomial case see McCullagh and Nelder
(1989, pp. 124–8). Although they show that there is (under some
restrictions) a model with
variance proportional to mean as in the quasibinomial model, note
that glm
does not compute maximumlikelihood estimates in that
model. The behaviour of S is closer to the quasi variants.
The design was inspired by S functions of the same names described in Hastie & Pregibon (1992).
McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Dobson, A. J. (1983) An Introduction to Statistical Modelling. London: Chapman and Hall.
Cox, D. R. and Snell, E. J. (1981). Applied Statistics; Principles and Examples. London: Chapman and Hall.
Hastie, T. J. and Pregibon, D. (1992) Generalized linear models. Chapter 6 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
nf < gaussian()# Normal family nf str(nf)# internal STRucture gf < Gamma() gf str(gf) gf$linkinv gf$variance(3:4) # == (.)^2 ## quasipoisson. compare with example(glm) counts < c(18,17,15,20,10,20,25,13,12) outcome < gl(3,1,9) treatment < gl(3,3) d.AD < data.frame(treatment, outcome, counts) glm.qD93 < glm(counts ~ outcome + treatment, family=quasipoisson()) glm.qD93 anova(glm.qD93, test="F") summary(glm.qD93) ## for Poisson results use anova(glm.qD93, dispersion = 1, test="Chisq") summary(glm.qD93, dispersion = 1) ## tests of quasi x < rnorm(100) y < rpois(100, exp(1+x)) glm(y ~x, family=quasi(var="mu", link="log")) # which is the same as glm(y ~x, family=poisson) glm(y ~x, family=quasi(var="mu^2", link="log")) ## Not run: glm(y ~x, family=quasi(var="mu^3", link="log")) # should fail y < rbinom(100, 1, plogis(x)) # needs to set a starting value for the next fit glm(y ~x, family=quasi(var="mu(1mu)", link="logit"), start=c(0,1))